1.1 Systems of Linear Equations
1.10Linear Models in Business, Science, and Engineering
1.2 Row Reduction and Echelon Forms
1.4 The Matrix Equation Ax = b
1.5 Solution Sets of Linear Systems
1.6 Applications of Linear Systems
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
2.3 Characterizations of Invertible Matrices
2.6 The Leontief Input-Output Model
2.7 Applications to Computer Graphics
3.1 Introduction to Determinants
3.2 Properties of Determinants
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces, and Linear Transformations
4.3 Linearly Independent Sets; Bases
4.5 The Dimension of a Vector Space
4.8 Applications to Difference Equations
4.9 Applications to Markov Chains
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.4 Eigenvectors and Lmear Transformations
5.6 Discrete Dynamical Systems
5.7 Applications to Differential Equations
5.8 Iterative Estimates for Eigenvalues
6.1 Inner Product, Length, and Orthogonality
6.6 Applications to Linear Models
6.8 Applications of Inner Product Spaces
7.1 Diagonalization of Symmetric Matrices
7.4 The Singular Value Decomposition
7.5 Applications to Image Processing and Statistics
Chapter 2 Supplementary Exercises
Chapter I Supplementary Exercises
Chapter 3 Supplementary Exercises
Chapter 4 Supplementary Exercises
Chapter 5 Supplementary Exercises